Periodic orbits of discrete and continuous dynamical systems via Poincar\'{e}-Miranda theorem
| Autor: | Gasull, Armengol, Mañosa, Víctor |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Discrete and Continuous Dynamical Systems -series B, 25 (2) (2020), 651-670 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3934/dcdsb.2019259 |
| Popis: | We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a one-parameter family of counterexamples to the discrete Markus-Yamabe conjecture (La Salle conjecture); the study of the low periods of a Lotka-Volterra-type map; the existence of three limit cycles for a piece-wise linear planar vector field; a new counterexample of Kouchnirenko's conjecture; and an alternative proof of the existence of a class of symmetric central configuration of the $(1+4)$-body problem. Comment: 26 pages, 7 figures |
| Databáze: | arXiv |
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